Deep Transfer Learning-Based Preconditioned GMRES Method for Acoustic Reverse Time Migration in the Frequency Domain

To alleviate the computational challenges of reverse time migration (RTM) in the frequency domain, this article constructs preconditioners based on the deep learning (DL) algorithm to accelerate Krylov subspace iterative method, typically generalized minimal residual (GMRES), for solving linear systems at different frequencies in wavefield extrapolation and applies transfer learning (TL) approaches to reduce the investment cost in the training process. To be specific, we utilize convolutional neural networks (CNNs) to learn the inverse characteristics of the impedance matrix to enhance the convergence of the iterative process and overcome the acceleration limitations imposed by traditional solvers. Then, the well-trained neural network is embedded into the preconditioning process of the GMRES method to ensure that the iterative vector can quickly converge to the true solution. In addition, for linear systems with different frequencies, a DL-preconditioner corresponding to a small frequency value is served as a pretrained model transferred to larger frequency scenarios, which greatly compresses the total training cost and further maximizes the practicality of the proposed method. Several numerical examples are employed to test the effectiveness of our approach and compared with some other classic solvers. Various results illustrate that the deep TL-preconditioned method can improve the computational efficiency of frequency-domain reverse time migration (RTM).